Electrodynamics I (2021)

Classical electrodynamics is one of the crown jewels of human achievement. What Newton's laws did for the understanding of motion, Maxwell's equations did for a far more mysterious set of phenomena - it unified apparently disconnected phenomena related to electricity, magnetism, and light, and contributed to the discovery of special relativity. Electrodynamics is the simplest gauge field theory - a mathematical structure with beautiful and useful features that is now used to understand essentially all physical phenomena. An area that remains relevant to research owing to its myriad applications, it serves as a starting point for more fancy theory.

Target Audience

This is the core course ED-1 or P-106 in the TIFR graduate school. If you already had a good course in electrodynamics before coming to TIFR, you should try to drop this course and directly take ED-2.

This page (and Moodle) will be updated regularly with course-related information. Please check frequently.

I am available over email (PLEASE include the tag "ED2021" in the subject line to ensure my spam filter doesn't reject it). You can send anonymous emails if you like. Comments, criticism, cat-gifs, all are welcome.

Administrivia

Time: 2-3 pm, Mondays, Wednesdays and Fridays

Venue: Online via zoom

First lecture: 17 Feb 2021

Instructor: Basudeb Dasgupta (A320)

Tutor: Krishnendu Maji

Course Contents

1. Preliminaries and Maxwell's equations (7 lectures)

2. Electrostatics in vacuum and materials (14 lectures)

3. Magnetostatics in vacuum and materials (6 lectures)

4. Time-varying E and B fields, and their properties (4 lectures)

5. Waves (8 lectures)

Suggested term paper topics: Fundamentals of ED, Optics, Acceleration, Trapping, Radiative Transfer, Waveguides, Membranes, Super/Sub-luminal Light, etc.

References

1. Modern Electrodynamics, Zangwill (Main Text; Beware of typos!)

2. Landau and Lifshitz Vol.2, Landau and Lifshitz

3. Landau and Lifshitz Vol.8, Landau, Lifshitz, and Pitaevskii

4. Classical Electrodynamics, Jackson

5. Feynman Lectures Vol.2, Feynman, Leighton, Sands

Problem Sets

PS1: Mathematical Background and Maxwell Equations

PS2: Electrostatics

PS3: Magnetostatics

PS4: Time varying E and B fields and Waves

All due by 7 June

Exams

Midterm: cancelled

Term Paper Presentation: June

Endterm: 29-30 May ; reports due by 13 June

Lecture Summaries

Day Zero (17 Feb): Course Overview

• Introductions

• Course contents and expectations (open & honest, aiming to understand just the basics - so that we can apply it to our real lives and research)

• Drop test

Lecture 1 (19 Feb): Preliminaries I

• Invitation to Electrodynamics

• Vectors, Tensors

• Curvilinear coordinates

Lecture 2 (22 Feb): Preliminaries II

• Derivatives, Integrals, and relevant identities and theorems

• Singularities

Lecture 3 (24 Feb): Preliminaries III

• Linearity and Fourier techniques

• Helmholtz Theorem

Lecture 4 (26 Feb): Maxwell's Equations I

• History, Charge, Current, Continuity

Lecture 5 (3 Mar): Maxwell's Equations II

• Units, Maxwell's Eqns, Particles vs Fields

Lecture 6 (8 Mar): Maxwell's Equations III

• Limits of this theory: Classical vs. Relativistic vs. Quantum, Monopole, Mass of photon, Axions?

• Macros vs Micro: Lorentz averaging

Lecture 7 (10 Mar): Maxwell's Equations IV

• Derive Maxwell's Equations?

• Revision

Lecture 8 (12 Mar): Electrostatics I

• Electrodynamics has 4 equations and 4 unknowns

• Electrostatic potential via Helmholtz thm

• Force, Torque, Work

• Earnshaw's thm

Lecture 9 (15 March): Electrostatics II

• Surface charge

• Matching conditions

• Force density

• Total energy, Self energy, Potential energy, Interaction energy

Lecture 10 (17 March): Electrostatics III

• Multipole expansion of 1/|r-r'|

• Identifying the primitive monopole, dipole, quadrupole, multipole of the charge distribution involving source coords

• How they couple to the observer coordinate and contribute to potential and work

Lecture 11 (19 March): Electrostatics IV

• Dipole, Point dipole

• Quadrupole

• Traceless multipoles

Lecture 12 (22 March): Electrostatics V

• Spherical multipoles

• Exterior and Interior expansions

Lecture 13 (24 March): Electrostatics VI

• Conductors

Lecture 14 (26 March): Electrostatics VII

• Dielectrics

Droptest (28 March; 1-5pm)

Lecture 15 (31 March): Electrostatics VIII

• Dielectrics

• Setting up electrostatic BVPs

Lecture 16 (5 April): Electrostatics IX

• BVPs

• Uniqueness

• Boundary Conditions

Lecture 17 (7 April): Electrostatics X

• Grounded conductors

• Method of Images

Lecture 18 (9 April): Electrostatics XI

• Numerical Solutions

Lecture 19 (12 April): Electrostatics XII

• Green's function

Lecture 20 (16 April): Electrostatics XIII

• Green's function

Lecture 21 (17 April): Electrostatics XIV

• Steady Currents

• Ohmic materials

• Battery and E fields

Lecture 22 (19 April): Magnetostatics I

• Helmholtz+Maxwell = Biot-Savart

• Summation problems = Biot-Savart

• Setting Up BVP using Scalar Potential and Matching Conditions

• Circular Ring

Lecture 23 (21 April): Magnetostatics II

• Helmholtz coil, Vector potential BVP in Coulomb gauge

• Multipole expansion and vanishing monopole

Lecture 24 (23 April): Magnetostatics III

• Multipole moments

• Dipole, Magnetic moment, g-2

• B fields do no work on moving charges

Lecture 25 (26 April): Magnetostatics IV

• • Force, Work, Energy

• What do B fields look like?

Lecture 26 (28 April): Magnetostatics V

• Magnetic materials

Lecture 27 (30 April): Magnetostatics VI

• Magnetic Materials

Lecture 28 (3 May): General EM fields I

• Displacement/Polarization current and magnetization

Lecture 29 (5 May): General EM field II

• Quasi-electrostatics and Quasi-magnetostatics

• Charge relaxation and Skin depth

Lecture 30 (7 May): General EM fields III

• Poynting vector, linear and angular momentum

Lecture 31 (8 May): General EM fields IV

• Energy-momentum conservation

• Covariant formulation

Lecture 32 (10 May): Waves I

• What are EM waves

Lecture 33 (12 May): Waves II

• Solving the vector wave equation

• Transverse waves and wavepackets

Lecture 34 (15 May): Waves III

• Gaussian beams

• Spherical waves

Lecture 35 (19 May): Waves IV

• Ponderomotive force

• Waves in simple media

Lecture 36 (21 May): Waves V

• Waves in simple media

Lecture 37 (22 May): Waves VI

• Dispersion

Lecture 38 (24 May): Waves VII

• TEM modes in coaxial cable

• Basic equations for TE, TM modes

Lecture 39 (26 May): Waves VIII

• Waveguides and Cavities

Lecture 40 (28 May): Summary

Endterm (29, 30 May)

Termpapers due on 13 June

End of Course (14June): Congratulations!